Here, we briefly introduce the naHEFT [1]}, [2]}.
In this framework, the BSM part of the Higgs potential is given by
\(V_{\rm {BSM}}(\Phi ) &= \frac{\xi }{4}\kappa _0\,[\mathcal {M}^2(\Phi )]^2 \ln \frac{\mathcal {M}^2(\Phi )}{\mu ^2},\) 
